The government provided affidavits regarding what was recovered during the raid. Trump could have provided an affidavit indicating, for instance, what items he believed were taken but not listed, or an affidavit explaining that he mixed up all those documents so that personal items (e.g., attorney-client privileged material or medical records) could be in the folders labeled classified , or maybe an affidavit stating that he had declassified the documents (but, as you and the 11th circuit have noted, that is a bit of a red herring). These sorts of proceedings do generally get resolved like summary judgment, so affidavits and then like work so long as it is clear that they could be converted to an admissible form and there are no objections to them. And, if needed, the court can also take live testimony.
There are two major things I think you have missed from beginning:
1) This involves a criminal proceeding in the investigatory phase. Almost all of the cases cited by Cannon (as I pointed out earlier in the thread), dealt with criminal proceedings that had completed. The ability to get such evidence returned or to refrain the government from using it is necessarily limited both due to equity and separation of powers.
2) Trump had the burden of demonstrating an possessory interest in the documents. He kept arguing the reverse, i.e., that the government had to prove that Trump didn't have a possessory interest. Cannon bought it. The 11th Circuit wasn't having it.